Hi Steve,
Estimation problems for the variance components in linear mixed models are usually occur for two reasons:
1. Due to model misspecification, i.e., using years instead of decades may show no variability in the slopes
2. Because the data do not support the assumptions of the linear mixed model (i.e., positive definite covariance matrix for the random-effects => increasing variance with time).
These may cause zero or even negative variance components. For more info you could take a look at Verbeke and Molenberghs (2000, Section 5.6) and Searle, Casella and McCullogh (1992, Section 3.5).
I don't know the exact formulation you are using, but maybe you could consider an analogue of you model using "gls", i.e.,
lme(..., random=~1|id) gls(..., corr=corCompSymm(form=~1|id))
The references mentioned above are:
@Book{verbeke.molenberghs:00,
author = {G. Verbeke and G. Molenberghs},
title = {Linear Mixed Models for Longitudinal Data},
year = {2000},
address = {New York},
publisher = {Springer-Verlag}
}@Book{searle.et.al:92,
author = {S. Searle and G. Cassela and C. McCulloch},
title = {Variance Components},
year = {1992},
address = {New York},
publisher = {Wiley}
}I hope it helps.
Best, Dimitris
---- Dimitris Rizopoulos Ph.D. Student Biostatistical Centre School of Public Health Catholic University of Leuven
Address: Kapucijnenvoer 35, Leuven, Belgium Tel: +32/16/396887 Fax: +32/16/337015 Web: http://www.med.kuleuven.ac.be/biostat/ http://www.student.kuleuven.ac.be/~m0390867/dimitris.htm
----- Original Message ----- From: "Steve Roberts" <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>
Sent: Tuesday, September 21, 2004 1:38 PM
Subject: [R] lme RE variance computation
As I understand it lme (in R v1.9.x) estimates random effect variances
on a log scale, constraining them to be positive. Whilst this seems
sensible, it does lead to apparently biased estimates if the variance is
actually zero - which makes our simulation results look strange. Whilst
we need to think a bit deeper about it - I still haven't got my head
around what a negative variance could mean - does anyone know a
way to take away the contraint and allowing zero or negative
variances?
Steve. Dr Steve Roberts [EMAIL PROTECTED]
Senior Lecturer in Medical Statistics, CMMCH NHS Trust and University of Manchester Biostatistics Group, 0161 275 5192 / 0161 276 5785
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